Hello all,
So I took the plunge and started trying to write optimized code in
Cython for my enumeration problem. The code can be found at
http://www.cems.uvm.edu/~voight/tr_data.spyx
http://www.cems.uvm.edu/~voight/totallyreal.py
and for the experts out there, I'd appreciate any feedback you can
give, including tricks and such. I also have a bunch of questions,
some of which are probably just due to my inexperience:
(1) At a certain moment in the algorithm, I need to test if a
polynomial with integer coefficients is squarefree (using exact
arithmetic). Is it acceptable practice to do this in a brutal way,
like:
import sage.rings.all PolynomialRing, IntegerRing, gcd
ZZx = PolynomialRing(IntegerRing(), 'x')
[...]
f = ZZx([...])
df = ZZx([...])
if gcd(f,df) <> 1:
What exactly is happening internally there? And what is the overhead
and effect on the timing?
(1a) Shouldn't the integer polynomial gcd work using modular
arithmetic to avoid coefficient blow-up? Or does it do this already?
(If gcd(f,g) mod p is 1 for p >> 0 then gcd(f,g) = 1, etc.)
(2) I have my Cython code in a tr_data.spyx file and my Python code in
a totallyreal.py file. How do I include the former into the latter--
or do I have to include both at the prompt?
(3) I understand that there is significantly more overhead when a
function is declared using
cdef incr(self)
instead of
def incr(self).
in tr_data.spyx. But if I do this, how do I then access incr in
totallyreal.py?
(4) Sometimes I need quite verbose output, when debugging and testing,
and othertimes I just want to turn it all off. Is there a way to set
a global parameter which controls the verbosity for several routines,
like the SetVerbose() in magma? Otherwise, I have to pass a "verbose"
parameter around...
(5) Is garbage collection automatic, or do I have to declare a __del__
function and do a sage_free?
(6) Craig, did you ever get around to making the line
K1._pari_().nfisisom(K2):
for testing isomorphism between number fields any less ugly?
Shouldn't it read
is_isomorphic(K1, K2)?
While you're at it, I need to be able to run an LLL-optimization
routine to speed up these functions: the function is called polred().
(7) What overhead happens in declaring a number field? Unless I am
reading this incorrectly, it now dominates my computation now!
sage: prun enumerate_totallyreal_fields(5,10^5)
390120 function calls (390117 primitive calls) in 8.774 CPU
seconds
Ordered by: internal time
ncalls tottime percall cumtime percall
filename:lineno(function)
971 3.795 0.004 3.795 0.004 {method 'nfinit' of
'sage.libs.pari.gen.gen' objects}
1979 1.024 0.001 1.901 0.001 {method 'is_irreducible'
of 'sage.rings.polynomial.polynomial_element.Polynomial' objects}
7600 0.403 0.000 0.710 0.000
polynomial_element_generic.py:946(__init__)
21686 0.332 0.000 0.381 0.000 rational_field.py:
120(__call__)
971 0.230 0.000 0.431 0.000 {method '_pari_' of
'sage.rings.polynomial.polynomial_element.Polynomial' objects}
111586 0.223 0.000 0.223 0.000 {isinstance}
8571 0.211 0.000 1.318 0.000 polynomial_ring.py:
162(__call__)
7581 0.197 0.000 0.197 0.000
{sage.libs.ntl.ntl.make_new_ZZX}
1996 0.169 0.000 0.419 0.000
polynomial_element_generic.py:878(list)
1 0.164 0.164 8.774 8.774 totallyreal.py:
24(enumerate_totallyreal_fields)
22151 0.142 0.000 0.226 0.000
polynomial_element_generic.py:1180(degree)
971 0.129 0.000 0.247 0.000
polynomial_element_generic.py:518(__init__)
45 0.123 0.003 0.123 0.003 {method 'nfisisom' of
'sage.libs.pari.gen.gen' objects}
2120 0.119 0.000 0.444 0.000 {method 'incr' of
'tr_data_spyx_0.tr_data' objects}
90 0.112 0.001 0.130 0.001 {method '_pari_' of
'sage.structure.sage_object.SageObject' objects}
971 0.101 0.000 0.922 0.001 number_field.py:
157(NumberField)
[...]
It'd better not be the case that invariants of the field are
automatically computed...!
(8) When printing a list of integers, why does it print vertically
instead of horizontally, i.e.
[1,
2,
...
]
instead of
[1, 2, ...]
or is this a vagary of Python?
Thanks,
John Voight
Assistant Professor of Mathematics
University of Vermont
[EMAIL PROTECTED]
[EMAIL PROTECTED]
http://www.cems.uvm.edu/~voight/
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